We generalize a support vector machine to a support spinor machine by using the mathematical structure of wedge product over vector machine in order to extend field from vector field to spinor field. The separated hyperplane is extended to Kolmogorov space in time series data which allow us to extend a structure of sup…
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48 results for “Support Analysis”
Average case analysis of Lasso under ultra-sparse conditionscond-mat.dis-nn
The Lasso performs well in ultra-sparse linear models with finite support size.
problem Performance analysis of Lasso in ultra-sparse linear models.
method Novel application of replica method from statistical physics, rigorous analysis of average case performance.
result Average performance of Lasso assessed without scaling assumptions, offering sample complexity bounds.
Meta-learning improves support recovery in high-dimensional PCA.
problem Support recovery in high-dimensional Principal Component Analysis.
method Meta-learning approach to reduce sample complexity and support recovery.
result Support recovery can be achieved with significantly fewer samples than traditional methods.
DeepSupp detects financial support levels using attention mechanisms.
problem Traditional SR identification methods fail to adapt to modern markets.
method Multi-head attention mechanisms, dynamic correlation matrices, DBSCAN clustering.
result DeepSupp outperforms six baseline methods across six financial metrics.
KSG mutual information estimator, which is based on the distances of each sample to its k-th nearest neighbor, is widely used to estimate mutual information between two continuous random variables. Existing work has analyzed the convergence rate of this estimator for random variables whose densities are bounded away fr…
These notes were originally written for the Stochastic Analysis Seminar in the Department of Operations Research and Financial Engineering at Princeton University, in February of 2011. The seminar was attended and supported by members of the Research Training Group, with the author being partially supported by NSF gran…
We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS…
Study optimal times to buy and sell stocks using support/resistance lines.
problem Optimal times to buy and sell stocks based on support and resistance lines.
method Mathematical model with probabilistic methods to solve optimal stopping problems.
result Best times to buy and sell stocks are determined by solving free boundary problems.
LFD-ProtoNet: Prototypical Network Based on Local Fisher Discriminant Analysis for Few-shot Learningcs.LG
A new method improves few-shot learning by combining ProtoNet with LFD.
problem Few-shot learning struggles with high variance support sets.
method Combines ProtoNet with Local Fisher Discriminant Analysis.
result Superior classification accuracy on miniImageNet and tieredImageNet.
The paper analyzes kNN density estimation's convergence rates under different conditions.
problem Analyzing convergence rates of kNN density estimation under bounded and unbounded support conditions.
method Examined two cases: bounded support with known and unknown support sets, and unbounded support with smooth density function.
result kNN density estimation is minimax optimal under certain conditions and better than kernel density estimation in some cases.
Analysis of the Relative Entropy Asymmetry in the Regularization of Empirical Risk Minimizationcs.IT
New regularization method reduces support of empirical risk minimization solutions.
problem Regularization in empirical risk minimization with relative entropy.
method Introduces Type-II regularization, characterizes solutions, analyzes properties of relative entropy.
result Type-II regularization collapses solution support into reference measure's support.
Proposes an L1-regularized functional SVM for binary classification with functional covariates.
problem Binary classification with multivariate functional covariates.
method L1-regularized functional support vector machine (SVM) with an accompanying algorithm.
result The proposed classifier performs well in prediction and feature selection.
We present a solution to an optimal stopping problem for a process with a wide-class of novel dynamics. The dynamics model the support/resistance line concept from financial technical analysis.
The paper proves consistency of archetypal analysis for multivariate data.
problem Finding optimal archetype points for multivariate data.
method Uses convex polytope to summarize data, proving consistency under specific distribution assumptions.
result Archetype points converge to optimal solution under certain conditions.
This study presents a rapid multiple incremental and decremental mechanism based on Weight-Error Curves (WECs) for support-vector analysis. Recursion-free computation is proposed for predicting the Lagrangian multipliers of new samples. This study examines Ridge Support Vector Models, subsequently devising a recursion-…
Integrating causal machine learning with inherently interpretable models for decision support.
problem Providing causal insights and decision support through machine learning models.
method Proposing an approach that integrates causal machine learning with inherently interpretable models.
result The proposed approach achieves competitive performance in prediction and what-if analysis while offering transparency on the system structure, causal relationships among variables, and functional forms connecting them.
We apply information-based complexity analysis to support vector machine (SVM) algorithms, with the goal of a comprehensive continuous algorithmic analysis of such algorithms. This involves complexity measures in which some higher order operations (e.g., certain optimizations) are considered primitive for the purposes …
Spectral features of the empirical moment matrix constitute a resourceful tool for unveiling properties of a cloud of points, among which, density, support and latent structures. It is already well known that the empirical moment matrix encodes a great deal of subtle attributes of the underlying measure. Starting from …
Study stability and bifurcation of liquid interfaces in cylindrical supports.
problem Stability and bifurcation of liquid interfaces in cylindrical support surfaces.
method Analysis of eigenvalues of the Jacobi operator, Plateau-Rayleigh instability, bifurcation theory.
result Conditions for the emergence of new morphologies and bifurcations from circular cylinders.
In many applications, input data are sampled functions taking their values in infinite dimensional spaces rather than standard vectors. This fact has complex consequences on data analysis algorithms that motivate modifications of them. In fact most of the traditional data analysis tools for regression, classification a…
We provide a formulation for Local Support Vector Machines (LSVMs) that generalizes previous formulations, and brings out the explicit connections to local polynomial learning used in nonparametric estimation literature. We investigate the simplest type of LSVMs called Local Linear Support Vector Machines (LLSVMs). For…
The paper analyzes sparse PCA for incomplete data and proves support recovery conditions.
problem Support recovery in sparse PCA with non-random missing data.
method Semidefinite relaxation of the -regularized PCA problem.
result Support of the sparse leading eigenvector can be recovered with high probability.
Yarbus' claim to decode the observer's task from eye movements has received mixed reactions. In this paper, we have supported the hypothesis that it is possible to decode the task. We conducted an exploratory analysis on the dataset by projecting features and data points into a scatter plot to visualize the nuance prop…
This technical report proves components consistency for the Doubly Stochastic Dirichlet Process with exponential convergence of posterior probability. We also present the fundamental properties for DSDP as well as inference algorithms. Simulation toy experiment and real-world experiment results for single and multi-clu…
A large number of algorithms in machine learning, from principal component analysis (PCA), and its non-linear (kernel) extensions, to more recent spectral embedding and support estimation methods, rely on estimating a linear subspace from samples. In this paper we introduce a general formulation of this problem and der…
Support vector regression (SVR) is one of the most popular machine learning algorithms aiming to generate the optimal regression curve through maximizing the minimal margin of selected training samples, i.e., support vectors. Recent researchers reveal that maximizing the margin distribution of whole training dataset ra…
We investigate the difference between using an penalty versus an constraint in generalized eigenvalue problems, such as principal component analysis and discriminant analysis. Our main finding is that an penalty may fail to provide very sparse solutions; a severe disadvantage for variable sel…
Behavioral analysis of support vector machine classifier with Gaussian kernel and imbalanced datacs.LG
Analyzes SVM classifier behavior with different parameters and data types.
problem Tuning SVM parameters for balanced and imbalanced data.
method Behavioral analysis of SVM with different parameters and data types, proposing a novel search algorithm.
result Proposed search algorithm reduces computational time and provides expected kernel function range.
Study shows Sobolev functions on non-compact manifolds can't be approximated by smooth compactly supported functions.
problem Sobolev functions on non-compact manifolds cannot be approximated by smooth compactly supported functions.
method Analysis of Sobolev spaces on non-compact manifolds.
result Proves the failure of the density of smooth compactly supported functions in Sobolev spaces on non-compact manifolds.
A new SVM method for predicting time series labels.
problem Learning to predict labels from high-dimensional time series data.
method Extended SVM concept to continuous time series data, formulated as a convex optimization problem.
result Empirical results show the algorithm's effectiveness for analyzing long-term multivariate data.
LOFT separates subspace rotation and transformation for orthogonal fine-tuning.
problem Conflating subspace rotation and transformation in orthogonal fine-tuning.
method LOFT explicitly separates subspace rotation and transformation, using task-aware support selection.
result LOFT recovers principal-subspace orthogonal adaptation and improves efficiency-performance trade-off.
In recent years, distance education has enjoyed a major boom. Much work at The Open University (OU) has focused on improving retention rates in these modules by providing timely support to students who are at risk of failing the module. In this paper we explore methods for analysing student activity in online virtual l…
Contextual bandit methods fail with deficient support data.
problem Learning from support-deficient data in contextual bandits.
method Three approaches to IPS-based learning: action space restriction, reward extrapolation, and policy space restriction.
result Systematic analysis and empirical evaluation of approaches to IPS-based learning.
Algorithm recovers sparse PCA support from incomplete data.
problem Sparse PCA with incomplete and noisy data.
method Semidefinite program (SDP) relaxation of non-convex -regularized PCA.
result SDP enables exact recovery of true support of sparse leading eigenvector.
With the widespread engineering applications ranging from artificial intelligence and big data decision-making, originally a lot of tedious financial data processing, processing and analysis have become more and more convenient and effective. This paper aims to improve the accuracy of stock price forecasting. It improv…
A new line search rule improves support recovery in high-dimensional data.
problem Support recovery in high-dimensional data analysis with penalty.
method Data-driven line search rule for adaptive step size determination.
result Proves error bound without restrictions on cost functional.
New models automate support group formation in online health communities.
problem Challenges in traditional support group formation methods for scalability, static categorization, and insufficient personalization.
method Two novel machine learning models: gDMR and gSTM, integrating user content, demographics, and network data.
result Models outperform baselines in predictive accuracy, semantic coherence, and internal group consistency.
In this article, a large dimensional performance analysis of kernel least squares support vector machines (LS-SVMs) is provided under the assumption of a two-class Gaussian mixture model for the input data. Building upon recent advances in random matrix theory, we show, when the dimension of data and their number $…
In this dissertation, the main goal is visualisation of financial time series. We expect that visualisation of financial time series will be a useful auxiliary for technical analysis. Firstly, we review the technical analysis methods and test our trading rules, which are built by the essential concepts of technical ana…
A Support-Set Algorithm for Optimization Problems with Nonnegative and Orthogonal Constraintsmath.OC
An algorithm simplifies optimization with nonnegative and orthogonal constraints.
problem Optimization problems with nonnegative and orthogonal constraints.
method Support-set algorithm exploiting structural sparsity.
result Global convergence to first-order stationary point with iteration complexity .
Estimates multiple related causal graphs with shared causal order.
problem Discovering multiple related Gaussian DAGs with shared causal order.
method Proposes a -regularized MLE for joint estimation of linear structural equation models.
result Joint estimator achieves better sample complexity and consistency in causal order recovery.
In conventional prediction tasks, a machine learning algorithm outputs a single best model that globally optimizes its objective function, which typically is accuracy. Therefore, users cannot access the other models explicitly. In contrast to this, multiple model enumeration attracts increasing interests in non-standar…
In this paper we show how to bypass the usual difficulties in the analysis of elliptic integrals that arise when solving period problems for minimal surfaces. The method consists of replacing period problems with ordinary Sturm-Liouville problems involving the support function. We give a practical application by provin…
The paper analyzes how the one-dimensional Wasserstein distance captures pointwise density differences in finite samples.
problem Uncertainty in identifying density differences when supports overlap and densities have substantial pointwise differences.
method Analysis using the Poisson process and neural spike train decoding.
result The one-dimensional Wasserstein distance highlights meaningful density differences related to both rate and support.
A novel approach to computing barycenters on graph-supported probability measures.
problem Computing weighted averages of measures on graphs.
method Dynamic optimal transport formulation on the simplex, gradient descent on the probability simplex.
result Intrinsic gradient descent provides a coherent framework for synthesizing and analyzing measures on graphs.
Paper supports robust estimation in regression with heavy-tailed errors.
problem Support estimation in high-dimensional heteroscedastic mean regression.
method Use of Huber loss function and adaptive LASSO penalty for robust estimation.
result Sign-consistency and optimal rates of convergence in norm.
Unique continuation property for measures in high dimensions.
problem Understanding the structure of measures in high-dimensional spaces.
method Analyzing locally uniformly distributed measures and their supports.
result Locally uniformly distributed measures satisfy a unique continuation property.
DBPA assesses LLM perturbations using frequentist hypothesis testing.
problem Quantifying input perturbation impacts on LLM outputs.
method DBPA reformulates perturbation analysis as frequentist hypothesis testing, using Monte Carlo sampling for empirical null and alternative distributions.
result DBPA provides interpretable p-values and scalar effect sizes for LLM perturbations.